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A345607 Numbers that are the sum of seven fifth powers in four or more ways.

%I A345607 #6 Jul 31 2021 16:25:13
%S A345607 893604,1117071,1182534,1414559,1629244,1933328,2280543,2586035,
%T A345607 2867074,3050644,3055295,3055977,3256432,3329360,3369543,3436058,
%U A345607 3551890,3576363,3896969,3914877,3930849,4055954,4087746,4088690,4093572,4096665,4098161,4104068,4104310
%N A345607 Numbers that are the sum of seven fifth powers in four or more ways.
%H A345607 Sean A. Irvine, <a href="/A345607/b345607.txt">Table of n, a(n) for n = 1..10000</a>
%e A345607 1117071 is a term because 1117071 = 1^5 + 2^5 + 6^5 + 7^5 + 7^5 + 14^5 + 14^5 = 2^5 + 2^5 + 4^5 + 6^5 + 10^5 + 12^5 + 15^5 = 3^5 + 4^5 + 7^5 + 7^5 + 7^5 + 7^5 + 16^5 = 3^5 + 5^5 + 6^5 + 6^5 + 7^5 + 8^5 + 16^5.
%o A345607 (Python)
%o A345607 from itertools import combinations_with_replacement as cwr
%o A345607 from collections import defaultdict
%o A345607 keep = defaultdict(lambda: 0)
%o A345607 power_terms = [x**5 for x in range(1, 1000)]
%o A345607 for pos in cwr(power_terms, 7):
%o A345607     tot = sum(pos)
%o A345607     keep[tot] += 1
%o A345607     rets = sorted([k for k, v in keep.items() if v >= 4])
%o A345607     for x in range(len(rets)):
%o A345607         print(rets[x])
%Y A345607 Cf. A345570, A345606, A345608, A345612, A345718, A346281.
%K A345607 nonn
%O A345607 1,1
%A A345607 _David Consiglio, Jr._, Jun 20 2021